Statistical patterns in primes
There is an interesting new result showing that the distribution of prime numbers obeys a modified version of Benford's Law. The result also shows that another sequence who's distribution is somehow fundamentally related to the distribution of primes, the 0s of the Reimann zeta function.
It is my feeling that results like this do not strongly affect the usefulness of prime number based cryptography algorithms like RSA. But this is just a guess on my part. Does anybody have a more definitive answer?